Actually in order for it to be a tank it has to be armored(or atleast have
some armor, see amx-50 and leopard 1), it has to be able to take out other tanks, it has to support infantry, and most importantly they have to be able to break through enemy defenses.
In this case it is self propelled anti-aircraft gun. It's mobile, it was intended shoot down lowflying planes, and it is suppose to protect the advancing tanks from air attacks. Also it only carries 4 20mm autoguns which would only be able to break the tracks of a tank and kills infantry and light vehicles. The only reason tank chassis' were used was because of cross country mobility as well being able to keep up with the armor and it was the easiest platform at the time to mount an AA gun on.
http://en.wikipedia.org/wiki/Wirbelwind